Type:	Package
Title:	Equality of 2 (or k) Continuous Univariate and Multivariate Distributions
Version:	0.9.2
Description:	We implement (or re-implements in R) a variety of statistical tools. They are focused on non-parametric two-sample (or k-sample) distribution comparisons in the univariate or multivariate case. See the vignette for more info.
License:	MIT + file LICENSE
Imports:	caret, dplyr, e1071, kernlab, magrittr, methods, pbapply, spatstat.univar, stats, transport
Suggests:	knitr, rmarkdown, testthat
VignetteBuilder:	knitr
biocViews:	Software, Infrastructure
Encoding:	UTF-8
RoxygenNote:	7.3.1
NeedsCompilation:	no
Packaged:	2024-05-28 06:12:51 UTC; hector
Author:	Hector Roux de Bezieux [aut, cre]
Maintainer:	Hector Roux de Bezieux <hector.rouxdebezieux@berkeley.edu>
Repository:	CRAN
Date/Publication:	2024-05-28 06:40:02 UTC

Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

Value

The pipe

Examples

2 %>% seq_len()

Classifier k-sample test

Description

Classifier k-sample test

Usage

classifier_test(
  x,
  y,
  split = 0.7,
  thresh = 0,
  method = "knn",
  control = caret::trainControl(method = "cv"),
  ...
)

Arguments

Details

See Lopez-Paz et .al for more background on those tests.

Value

A list containing the following components:

• statistic the value of the test statistic.

• p.value the p-value of the test.

References

Lopez-Paz, D., & Oquab, M. (2016). Revisiting Classifier Two-Sample Tests, 1–15. Retrieved from http://arxiv.org/abs/1610.06545

Examples

 x <- matrix(c(runif(100, 0, 1),
               runif(100, -1, 1)),
             ncol = 2)
 y <- matrix(c(runif(100, 0, 3),
               runif(100, -1, 1)),
             ncol = 2)
 classifier_test(x, y)

Weighted KS Test

Description

Weighted Kolmogorov-Smirnov Two-Sample Test with threshold

Usage

ks_test(x, y, thresh = 0.05, w_x = rep(1, length(x)), w_y = rep(1, length(y)))

Arguments

Details

The usual Kolmogorov-Smirnov test for two vectors X and Y, of size m and n rely on the empirical cdfs E_x and E_y and the test statistic

D = sup_{t\in (X, Y)} |E_x(x) - E_y(x))

. This modified Kolmogorov-Smirnov test relies on two modifications.

• Using observation weights for both vectors X and Y: Those weights are used in two places, while modifying the usual KS test. First, the empirical cdfs are updates to account for the weights. Secondly, the effective sample sizes are also modified. This is inspired from https://stackoverflow.com/a/55664242/13768995, using Monahan (2011).

• Testing against a threshold: the test statistic is thresholded such that D = max(D - thresh, 0). Since 0\le D\le 1, the value of the threshold is also between 0 and 1, representing an effect size for the difference.

Value

A list with class "htest" containing the following components:

• statistic the value of the test statistic.

• p.value the p-value of the test.

• alternative a character string describing the alternative hypothesis.

• method a character string indicating what type of test was performed.

• data.name a character string giving the name(s) of the data.

References

Monahan, J. (2011). Numerical Methods of Statistics (2nd ed., Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511977176

Examples

 x <- runif(100)
 y <- runif(100, min = .5, max = .5)
 ks_test(x, y, thresh = .001)

Perform the Maximum Mean Discrepancy unbiased bootstrap test

Description

Maximum Mean Discrepancy Unbiased Test

Usage

mmd_test(
  x,
  y,
  kernel = "rbfdot",
  type = ifelse(min(nrow(x), nrow(y)) < 1000, "unbiased", "linear"),
  null = c("permutation", "exact"),
  iterations = 10^3,
  frac = 1,
  ...
)

Arguments

Details

This computes the MMD^2u unbiased statistic or the MMDl linear statistic from Gretton et al. The code relies on the pairwise_kernel function from the python module sklearn. To list the available kernels, see the examples.

Value

A list containing the following components:

• statistic the value of the test statistic.

• p.value the p-value of the test.

References

Gretton, A., Borgwardt, K., Rasch, M. J., Schölkopf, B., & Smola, A. (2012). A Kernel Two-Sample Test Journal of Machine Learning Research (2012)

Examples

x <- matrix(rnorm(1000, 0, 1), ncol = 10)
y <- matrix(rnorm(1000, 0, 2), ncol = 10)
mmd_test(x, y)
mmd_test(x, y, type = "linear")
x <- matrix(rnorm(1000, 0, 1), ncol = 10)
y <- matrix(rnorm(1000, 0, 1), ncol = 10)
 # Set iterations to small number for runtime
 # Increase for more accurate results
mmd_test(x, y, iterations = 10^2)

Stouffer

Description

Stouffer's Z-score method

Usage

stouffer_zscore(pvals, weights = rep(1, seq_along(pvals)), side = "two")

Arguments

Details

Given a set of i.i.d p-values and associated weights, it combines the p-values p_i. Letting \phi be the standard normal cumulative distribution function and Z_i =\phi^{-1} (1-p_i), the meta-analysis Z-score is

Z = (\sum w_i Z_i) * (\sum (w_i)^2)^(-1/2)

Value

A list containing the following components:

• statistic the value of the test statistic.

• p.value the p-value of the test.

References

Samuel Andrew Stouffer. Adjustment during army life. Princeton University Press, 1949.

Examples

 pvals <- runif(100, 0, 1)
 weights <- runif(100, 0, 1)
 stouffer_zscore(pvals, weights)

Permutation test based on Wasserstein distance

Description

Permutation test based on Wasserstein distance

Usage

wasserstein_permut(
  x,
  y,
  iterations = 10^4,
  fast = nrow(x) + nrow(y) > 10^3,
  S = NULL,
  ...
)

Arguments

Value

A list containing the following components:

• statistic the Wasserstein distance between x and y.

• p.value the p-value of the permutation test.

Examples

 x <- matrix(c(runif(100, 0, 1),
               runif(100, -1, 1)),
             ncol = 2)
 y <- matrix(c(runif(100, 0, 3),
               runif(100, -1, 1)),
             ncol = 2)
 # Set iterations to small number for runtime
 # Increase for more accurate results
 wasserstein_permut(x, y, iterations = 10^2)